Here's a clue. You are living in the States but your visa status does not allow you to live there. You are therefore non resident in the USA. That means you must be resident somewhere else, ie. the UK. That's why you can't get insurance. Think about it. If everyone living in the US didn't want to pay for medical bills, they could all go out and get travel insurance for a fraction of the cost. You can therefore only obtain insurance in the UK for your travels which will, of course, be limited to 31 or so days in a year. If you tried to claim against it, the first thin they will want to see is your travel and flight booking details to confirm that you have not lived in the country you are claiming for for more than the maximum period.